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Chao L.,Nanyang Technological University | Kwak S.K.,Ulsan National Institute of Science and Technology | Ansumali S.,Engineering Mechanics Unit
International Journal of Modern Physics C | Year: 2014

We propose a modified direct simulation Monte Carlo (DSMC) method, which extends the validity of DSMC from rarefied to dense system of hard spheres (HSs). To assess this adapted method, transport properties of hard-sphere (HS) systems have been predicted both at dense states as well as dilute, and we observed the excellent accuracy over existing DSMC-based algorithms including the Enskog theory. The present approach provides an intuitive and systematic way to accelerate molecular dynamics (MD) via mesoscale approach. © 2014 World Scientific Publishing Company.

Raja R.V.,National Institute of Technology Tiruchirappalli | Subramanian G.,Engineering Mechanics Unit | Koch D.L.,Cornell University
Journal of Fluid Mechanics | Year: 2010

The behaviour of an isolated nearly spherical drop in an ambient linear flow is examined analytically at small but finite Reynolds numbers, and thereby the first effects of inertia on the bulk stress in a dilute emulsion of neutrally buoyant drops are calculated. The Reynolds numbers, Re = ya 2p/μ and Re =ya2p/μ are the relevant dimensionless measures of inertia in the continuous and disperse(drop) phases, respectively. Here, a is the drop radius, is the shear rate, is the common density and and are, respectively, the viscosities of the drop and the suspending fluid. The assumption of nearly spherical drops implies the dominance of surface tension, and the analysis therefore corresponds to the limit of the capillary number(Ca) based on the viscosity of the suspending fluid being small but finite; in other words, Ca ≤ 1, where Ca =μay/T, T being the coefficient of interfacial tension. The bulk stress is determined to O(øRe) via two approaches. The first one is the familiar direct approach based on determining the force density associated with the disturbance velocity field on the surface of the drop; the latter is determined to O(Re) from a regular perturbation analysis. The second approach is based on a novel reciprocal theorem formulation and allows the calculation, to O(øRe), of the drop stresslet, and hence the emulsion bulk stress, with knowledge of only the leading-order Stokes fields. The first approach is used to determine the bulk stress for linear flows without vortex stretching, while the reciprocal theorem approach allows one to generalize this result to any linear flow. For the case of simple shear flow, the inertial contributions to the bulk stress lead to normal stress differences(N 1, N2) at O(øRe), where (≤1) is the volume fraction of the disperse phase. Inertia leads to negative and positive contributions, respectively, to N1 and N2 at O(øRe). The signs of the inertial contributions to the normal stress differences may be related to the O(ReCa) tilting of the drop towards the velocity gradient direction. These signs are, however, opposite to that of the normal stress differences in the creeping flow limit. The latter are O(Ca) and result from an O(Ca2) deformation of the drop acting to tilt it towards the flow axis. As a result, even a modest amount of inertia has a significant effect on the rheology of a dilute emulsion. In particular, both normal stress differences reverse sign at critical Reynolds numbers(Re c) of O(Ca) in the limit Ca≤1. This criterion for the reversal in the signs of N1 and N2 is more conveniently expressed in terms of a critical Ohnesorge number(Oh) based on the viscosity of the suspending fluid, where Oh = μ/(paT)1/2. The critical Ohnesorge number for a sign reversal in N1 is found to be lower than that for N2, and the precise numerical value is a function of Λ In uniaxial extensional flow, the Trouton viscosity remains unaltered at O(øRe), the first effects of inertia now being restricted to O(Re 3/2). The analytical results for simple shear flow compare favourably with the recent numerical simulations of Li & Sarkar (J. Rheol., vol. 49, 2005, p. 1377). Copyright © Cambridge University Press 2010.

Ansumali S.,Engineering Mechanics Unit
Communications in Computational Physics | Year: 2011

This work proposes an extension to Boltzmann BGK equation for dense gases. The present model has an H-theorem and it allows choice of the Prandtl number as an independent parameter. I show that similar to Enskog equation this equation can reproduce dynamics of dense gases. © 2011 Global-Science Press.

Koch D.L.,Cornell University | Subramanian G.,Engineering Mechanics Unit
Annual Review of Fluid Mechanics | Year: 2011

Experimental observations indicate that, at sufficiently high cell densities, swimming bacteria exhibit coordinated motions on length scales (10 to 100 μ) that are large compared with the size of an individual cell but too small to yield significant gravitational or inertial effects. We discuss simulations of hydrodynamically interacting self-propelled particles as well as stability analyses and numerical solutions of averaged equations of motion for low Reynolds number swimmers. It has been found that spontaneous motions can arise in such systems from the coupling between the stresses the bacteria induce in the fluid as they swim and the rotation of the bacteria due to the resulting fluid velocity disturbances. © 2011 by Annual Reviews. All rights reserved.

Prasianakis N.,Paul Scherrer Institute | Ansumali S.,Engineering Mechanics Unit
Communications in Computational Physics | Year: 2011

The exact solution to the hierarchy of nonlinear lattice Boltzmann kinetic equations, for the stationary planar Couette flow for any Knudsen number was presented by S. Ansumali et al. [Phys. Rev. Lett., 98(2007), 124502]. In this paper, simulation results at a non-vanishing value of the Knudsen number are compared with the closed-form solutions for the higher-order moments. The order of convergence to the exact solution is also studied. The lattice Boltzmann simulations are in excellent agreement with the exact solution. © 2011 Global-Science Press.

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